Hopf bifurcation in two-component flow
Abstract
The stability of viscosity-stratified bicomponent flow has been studied by long wave asymptotics, by short wave asymptotics and numerically. These studies have shown that interfacial instabilities arise from the viscosity difference between the two fluids. If the surface tension between the fluids is non-zero, then Hopf type bifurcations leading to traveling interfacial waves are expected. This paper proves a rigorous theorem establishing the existence of bifurcating solutions of this nature.
- Publication:
-
Technical Summary Report Wisconsin Univ
- Pub Date:
- May 1984
- Bibcode:
- 1984wisc.reptS....R
- Keywords:
-
- Asymptotic Methods;
- Branching (Mathematics);
- Flow Stability;
- Fluid Flow;
- Liquid-Liquid Interfaces;
- Stratification;
- Viscosity;
- Boundaries;
- Couette Flow;
- Interfacial Tension;
- Normality;
- Periodic Variations;
- Reynolds Number;
- Theorem Proving;
- Traveling Waves;
- Walls;
- Wavelengths;
- Fluid Mechanics and Heat Transfer